Which of these relations on {0, 1, 2, 3} are equivalence ?relations

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

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Q: Let A = {0,1,2,3} and R be the relation on A given by R =…

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Q: 9.3. Let A = {0,1}. Determine all the relations on A.

A: The objective is to determine all the relations on A.

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

Q: Let R1 = {(1,1), (2,2)} and R2 = {(1,1), (1, 2)} be relations on A = {1,2}. Then R1 UR

A: In this question given that two sets R1 and R2 and we find the unions  of these sets and relation of…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

Q: Give an example of numbers x, y such that |x| + |y| = x − y.

A: Given that: give an example of numbers x, y such that |x| + |y| = x − y.

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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Q: Check whether Ris reflexive, symmetric or transitive and hence determine whether the relation Ris…

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Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…

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Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

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Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

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Q: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

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Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

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Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

Q: Let A- {#, 7, x} and let R be the relation on. A given by R {(7, 7). (#, #)}. Prove or disprove…

A: Transitivity is a property of verbs that relates to whether a verb can take objects and how many…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that R ∪ S is…

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Q: 3) Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the…

A: Given A=1,2,3,4,5,6,7,8 contains the ordered pair 2,3,3,24,7,5,5 and 8,7 Since, for the diagonal…

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

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Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3),(4,5)} on the set A =…

A: Let R be a binary relation on a set A. R is said to be  reflexive if for all . R is said to be…

Q: Let A = {#, 7, x} and let R be the relation on A given by R = {(7, 7), (#, #)}

A: R is  said to be reflexive relation on A if for all x in A, xRx holds.  R is said to be symmetric…

Q: A = {1,2,3,4,6,8,12} a.) Relation on Z Refleksif Symmetric Transitive

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Q: * ?Which of these relations on {0, 1, 2, 3} are equivalence relations a) {(0, 0), (1, 1), (2, 2),…

A: A and C are the equivalence relations

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3)} on the set A = {1,2,3,4,5}.…

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Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: Which of these relations on {0, 1, 2, 3} are * ?equivalence relations а) ((0, 0), (1, 1), (2, 2),…

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